A Note on the Analytic Structure of Celestial Amplitudes

TL;DR

This paper investigates the analytic structure of celestial amplitudes in massless effective field theories, revealing complex features like branch cuts through RGE resummation, and highlights the limitations of fixed-order loop analysis.

Contribution

It demonstrates that resumming leading logarithmic contributions via RGEs uncovers richer analytic structures in celestial amplitudes, advancing understanding beyond fixed-order approximations.

Findings

Fixed-order loops produce multipoles on the negative β-plane.

Resummation with RGEs reveals branch cuts in celestial amplitudes.

Certain RGE relations can generate multipoles or shifted poles.

Abstract

Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on "ordinary" amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of great interest and need to be better understood. In this paper, we critically examine the analytic structure of celestial amplitudes in a massless low-energy effective field theory. We find that, fixed-order loop contributions, which generate multipoles on the negative $\beta$-plane, in general do not provide an accurate description of the analytic structure of celestial amplitudes. By resumming over the leading logarithmic contributions using renormalization group equations (RGEs), we observe much richer analytic structures, which generally contain branch cuts. It is also possible to generate multipoles or shifted single poles if the RGEs satisfy certain relations. Including sub-leading logarithmic contributions is expected to introduce additional corrections to the picture. However, without a new approach, it is difficult to make a general statement since the analytic form of the Mellin transform is challenging to obtain.